In a nonstick 12-inch skillet, heat 1 teaspoon oil over medium-high heat until very hot. Add the chicken and cook until the chicken is golden brown and loses its pink color throughout, 4 to 5 minutes per side. Remove the chicken from the skillet and reduce the heat to medium. Add the remaining 2 teaspoons oil to the skillet. Add the apples and onions. Cook, stirring, until tender. Stir in the curry powder and salt; cook 1 minute. Stir in the chutney and 1/2 cup water. Heat to boiling and boil for 1 minute. Spoon the sauce equally over the chicken breasts.